Zhu Shanqing, who owns a yarn-spinning factory in Hangzhou in China's Zhejiang province, is struggling with rising costs for labor, energy and land. So he is boxing up some of his spindles and moving.

To South Carolina.

Mr. Zhu is one of a growing number of Asian textile manufacturers setting up production in the U.S. Southeast to save money as salaries, energy and other costs rise at home. His company, Keer Group Co., has...